LEADER 02617oam 2200445 450 001 996418195703316 005 20210506102323.0 010 $a3-030-54154-1 024 7 $a10.1007/978-3-030-54154-5 035 $a(CKB)4100000011586021 035 $a(DE-He213)978-3-030-54154-5 035 $a(MiAaPQ)EBC6404862 035 $a(PPN)251087115 035 $a(EXLCZ)994100000011586021 100 $a20210506d2020 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometry and analysis of metric spaces via weighted partitions /$fJun Kigami 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (VIII, 164 p. 10 illus.) 225 1 $aLecture Notes in Mathematics ;$vVolume 2265 311 $a3-030-54153-3 330 $aThe aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text: It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic. Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights. The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of p-energies associated with the partition and the weight function corresponding to the metric. These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas. 410 0$aLecture notes in mathematics ;$vVolume 2265. 606 $aConformational analysis 615 0$aConformational analysis. 676 $a541.223 700 $aKigami$b Jun$065976 801 0$bCaPaEBR 801 1$bCaPaEBR 801 2$bUtOrBLW 906 $aBOOK 912 $a996418195703316 996 $aGeometry and Analysis of Metric Spaces via Weighted Partitions$91768616 997 $aUNISA